Low-complexity quantum codes designed via codeword-stabilized framework

We consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a graph and a binary code. For codes that can be obtained from a given graph, we give several upper bounds on the distance of a generic (additive or non-additive) CWS code, and the lower Gilbert-Varshamov bound for the existence of additive CWS codes. We also consider additive cyclic CWS codes and show that these codes correspond to a previously unexplored class of single-generator cyclic stabilizer codes. We present several families of simple stabilizer codes with relatively good parameters.Comment: 12 pages, 3 figures, 1 tabl

Coordinated optimization of visual cortical maps : 1. Symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of orientation columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about a hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference. From basic symmetry assumptions we obtain a comprehensive phenomenological classification of possible inter-map coupling energies and examine representative examples. We show that each individual coupling energy leads to a different class of OP solutions with different correlations among the maps such that inferences about the optimization principle from map layout appear viable. We systematically assess whether quantitative laws resembling experimental observations can result from the coordinated optimization of orientation columns with other feature maps

Coordinated optimization of visual cortical maps (I) Symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of OP columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about an hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference.Comment: 90 pages, 16 figure

Towards a Simplified Dynamic Wake Model using POD Analysis

We apply the proper orthogonal decomposition (POD) to large eddy simulation data of a wind turbine wake in a turbulent atmospheric boundary layer. The turbine is modeled as an actuator disk. Our analyis mainly focuses on the question whether POD could be a useful tool to develop a simplified dynamic wake model. The extracted POD modes are used to obtain approximate descriptions of the velocity field. To assess the quality of these POD reconstructions, we define simple measures which are believed to be relevant for a sequential turbine in the wake such as the energy flux through a disk in the wake. It is shown that only a few modes are necessary to capture basic dynamical aspects of these measures even though only a small part of the turbulent kinetic energy is restored. Furthermore, we show that the importance of the individual modes depends on the measure chosen. Therefore, the optimal choice of modes for a possible model could in principle depend on the application of interest. We additionally present a possible interpretation of the POD modes relating them to specific properties of the wake. For example the first mode is related to the horizontal large scale movement. Besides yielding a deeper understanding, this also enables us to view our results in comparison to existing dynamic wake models

Design Optimization Of Datapath Transmitter In Bluetooth Baseband Controller

A Bluetooth baseband controller is placed in the physical layer of the Bluetooth Protocol stack to manage all the physical channels and links like error correction, hop selection, security and data whitening. The baseband handles the packets and does the inquiry for the Bluetooth devices in the area. The optimization of the performance is needed but it is of a trade off with the area and power consumption of the device. The bigger the design, the more the power being consumed. In this thesis, the objective is to optimize the design of the transmitter in the datapath of the Bluetooth baseband controller. It is also part of the objective to improve the RC delay of the worst path timing. The inherited codes need to be verified with a test bench on Model Sim first. Then, a synthesis process is being done using the Synopsys tool in order to generate a netlist. The netlist is then being translated into physical implementation of the logic and the layout is formed. Then, the optimization process starts again from the VHDL code to the layout process. The synthesized results are first being compared with the results from the IC Compiler. The results of the synthesized results before and after optimization is being compared as well. It is shown that the optimized design has a larger area and power consumption of 75023.627147 square micron and 18.2595 mW but the timing in the worst path is significantly improved from 4 ps to 390 ps. The transmitter is able to operate at 200 MHz from the constraint set and the operating voltage is at 1.62 V. Thus, a tradeoff with the area and power consumption is in place if optimization on the timing performance is done. The focus of this project is on the performance of the design

비정상유동이 조류발전단지 배치최적화에 미치는 영향

학위논문(석사) -- 서울대학교대학원 : 공과대학 건설환경공학부, 2022.2. 황진환.Due to the global climate crisis and the air pollution, demand on the renewable energy is consequently increasing as one of the main efforts. Wind and solar energy are taking the lead on the renewable energy industry, and as of the next competitive resource, tidal power is estimated to have a huge potential, thanks to its high energy density and easily predictable characteristics. Tidal power has not reached the practical level yet, due to financial challenges. In terms of reducing the cost and reach the competitive level of LCOE, the power extraction should be maximized within the constraints by conducting layout optimization of the turbines deployed, hence, understanding, and predicting the algorithm for layout optimization is necessary. The layout optimization for the tidal turbine is somewhat sophisticated, due to the unsteady tidal current condition in the nature, hence previous studies have found the problem under the steady condition. However, since the unsteadiness is a critical feature of the tidal current, there needs a study on the distinctive optimization characteristics under the unsteady condition. This study aims to find the tidal turbine farm layout optimization problem under the simplified unsteady tidal current condition in the nature and identify if the tidal turbine farm layout optimization procedure under unsteady condition can converges to find the global optimum. A number of numerical experiments were handled during the study to find the general trend/pattern of convergence to the global optimum under the various unsteady condition, with variation in the amplitude and the direction. The study first demonstrated the difference in the wake profile and the energy production of a single turbine under steady & unsteady flow, to be used as the basic assumption when figuring out the characteristics of layout optimization procedure under unsteady condition. The study also demonstrated the insight of the optimized layout and the minimum velocity threshold that enables the optimization to converge to the globally optimized layout at a given tolerance under steady condition. Finally, generalization of the strategy for the tidal turbine farm layout optimization under the unsteady flow was presented by finding the difference in the optimization procedure between steady & unsteady flow. It has been discovered that optimal layout under unidirectional, unsteady flow condition is similar to the optimal layout under steady condition when it satisfies the minimum velocity threshold condition. However, optimal layout under bidirectional conditions was totally different to the optimal layout under unidirectional conditions, to consider the wake effect from both directions. Under the bidirectional flow condition, the turbines were found to be staggered with respect to each other in order to take advantage of local speedups between upwind turbines. The numerical experiments were performed with OpenTidalFarm, an open-source solver for specific PDE-constrained, gradient-based optimization problems, especially those related to tidal farm design. The simulation domain was described as a rectangular farm, PDE is given as two-dimensional nonlinear shallow water equations, total power output is the target functional to be maximized, and turbine was parameterized as a bump function. Adjoint method was used as to compute the gradient for the optimization problem.세계적인 기후 위기와 대기 오염으로 인해, 재생 에너지에 대한 수요가 증가하고 있다. 풍력과 태양광 발전이 신재생에너지 산업을 선도하고 있으며, 조류 발전은 높은 에너지 밀도와 예측 가능한 특성으로 인해 앞으로의 잠재력이 클 것으로 추정된다. 조류 발전은 아직 가격 경쟁의 측면에서 실용화 수준에 이르지 못했다. 가격 경쟁력을 확보하기 위한 비용절감의 수단으로는 전력 추출 극대화를 위한 노력이 필요하며, 이에 제약 조건 내에서의 터빈 배치 최적화를 위한 알고리즘에 대한 이해가 선행되어야 한다. 조류발전 단지 배치 최적화에 대한 연구는 기존에 다수 진행되어 왔으나, 비정상 유동에서의 최적화 해를 도출하는 것이 다소 복잡해 정상유동 상태의 가정이 주를 이루었다. 그러나, 조류는 달과 태양의 기조력에 의한 조류에 의해 발생하는 현상임에 따라, 비정상 유동이라는 특성이 크게 작용하는 바, 본 연구에서는 이러한 특성을 반영한 배치 최적화 연구가 진행되었다. 따라서 본 연구는 비정상 유동 하에서의 조류발전단지 배치 최적화에 관한 이해를 기반으로 이 때의 민감도 기반 최적화의 해가 전역 최적해에 수렴하는가를 수치실험을 통해 확인하는 것을 목적으로 하였다. 다양한 진폭과 방향 등의 조건에서 수백개의 수치실험이 이루어졌으며 이를 통해 비정상 유동 하에서의 조류발전단지 배치 최적화에 대한 일반적인 추세와 최적해를 확인하였다. 먼저, 정상 유동과 비정상 유동 각각에 단일 터빈을 두어 각 조건 하에서의 후류 형태와 에너지 생산량 차이를 확인하였다. 또한 정상 유동 하에서의 최적 배치 형태와 최적해에 도달할 수 있는 임계 속도 값을 도출하여 비정상 유동 하에서의 수치실험에 선행 가정으로 사용될 수 있도록 하였다. 이러한 실험 결과들을 바탕으로 비정상 유동 하에서의 조류발전단지 배치 최적화에 대한 일반적인 추세와 최적해를 확인할 수 있었다. 비정상 단방향 유동의 경우에는 임계 속도 조건을 만족하였을 때 정상 유동 하에서의 최적 배치와 비슷한 형태를 보였지만, 비정상 양방향 유동의 경우에는 터빈이 교차 배치된 형태를 최적 배치로 갖는 것을 알 수 있었다. 수치실험에는 파이썬 기반 오픈소스 소프트웨어인 OpenTidal Farm이 사용되었다. 수치실험은 직사각형 조류발전 단지 내에서 이루어졌으며, 편미분 방정식은 2차원 천수방정식을 사용했고, 목적함수는 총에너지 추출량으로 구성되었다. 또한, 터빈은 민감도 기반 최적화에 적합하게끔 범프함수로 매개변수화 되어 실험에 사용되었다.ABSTRACT i TABLE OF CONTENTS iv List of Figures vii List of Symbol xi CHAPTER 1. INTRODUCTION 1 1.1 General introduction 1 1.2 Objective 2 CHAPTER 2. THEORETICAL BACKGROUDS 7 2.1 General evolution of the renewable energy 7 2.2 Tidal turbine farm 10 2.2.1 The physics of tide 10 2.2.2 The physics of tidal currents - unsteadiness 13 2.2.3 Tidal turbine 15 2.2.4 Tidal energy resources in Korea 17 2.3 Shallow water equation (SWE) 19 2.4 Gradient-based optimization using adjoint method 21 2.4.1 Problem formulation 22 2.4.2 The adjoint method 22 CHAPTER 3. METHODOLOGY 25 3.1 Numerical model description 25 3.1.1 The design parameters 25 3.1.2 The PDE constraints 25 3.1.3 The turbine parameterization 26 3.1.4 The functional of interest 27 3.1.5 Box and inequality constraints 27 3.1.6 Optimization algorithm 28 3.2 Experiment overview 29 3.2.1 Experiment procedure 29 3.2.2 Experimental flow chart 31 3.3 Simulation set-up 31 3.3.1 Mesh domain 31 3.3.2 Boundary condition 33 3.3.3 Parameter settings 36 CHAPTER 4. Test cases, Results and Discussions 39 4.1 Pilot Test 1: Steady & Unsteady flow impact on a single turbine 39 4.1.1 Wake behavior 39 4.1.2 comparison criterion between steady and unsteady flow based on the energy production 46 4.1.3 Conclusion of Pilot test 1 48 4.2 Pilot Test 2: Minimum velocity threshold (MVT) to converge to QGO and the concept of the optimized layout 49 4.2.1 Test cases 49 4.2.2 Finding minimum threshold of velocity (MVT) 51 4.2.3 Insights on the optimized layout 55 4.2.4 Conclusion of Pilot test 2 57 4.3 Main test: Effect of unsteadiness in the optimization procedure compared to the steady condition 59 4.3.1 Test cases 59 4.3.2 Optimal layout for each flow conditions 62 4.3.3 Strategy to obtain QGO for bidirectional flow condition 70 4.3.4 Conclusion of Main test 71 CHAPTER 5. Conclusions 73 REFERENCES 76 국문초록 80석

Hyperbolic planforms in relation to visual edges and textures perception

We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g. optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in [1, 2] to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.Comment: 34 pages, 11 figures, 2 table